{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ERAHH4HLOUZV6E4I7KL3AZ47QP","short_pith_number":"pith:ERAHH4HL","canonical_record":{"source":{"id":"1803.08881","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-03-23T16:55:29Z","cross_cats_sorted":[],"title_canon_sha256":"6cff6fbc0d7ea809a1460a9e403efc846d5ccd646cd8df5930ea819ff3bc3226","abstract_canon_sha256":"f62b276b06576984343e6eac4948220295a0d86ba815b13ff97def2bc738c070"},"schema_version":"1.0"},"canonical_sha256":"244073f0eb75335f1388fa97b0679f83eea5e05e1e535e54cfd0f6ab1aa6b4e9","source":{"kind":"arxiv","id":"1803.08881","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.08881","created_at":"2026-05-18T00:12:48Z"},{"alias_kind":"arxiv_version","alias_value":"1803.08881v2","created_at":"2026-05-18T00:12:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.08881","created_at":"2026-05-18T00:12:48Z"},{"alias_kind":"pith_short_12","alias_value":"ERAHH4HLOUZV","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"ERAHH4HLOUZV6E4I","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"ERAHH4HL","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ERAHH4HLOUZV6E4I7KL3AZ47QP","target":"record","payload":{"canonical_record":{"source":{"id":"1803.08881","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-03-23T16:55:29Z","cross_cats_sorted":[],"title_canon_sha256":"6cff6fbc0d7ea809a1460a9e403efc846d5ccd646cd8df5930ea819ff3bc3226","abstract_canon_sha256":"f62b276b06576984343e6eac4948220295a0d86ba815b13ff97def2bc738c070"},"schema_version":"1.0"},"canonical_sha256":"244073f0eb75335f1388fa97b0679f83eea5e05e1e535e54cfd0f6ab1aa6b4e9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:48.230068Z","signature_b64":"Jt45jYbllqchnhZFS6+AtgwFYHOg6Uy+rS9HxhG+exeWPAMTd7qwXf+BOGfc7furMZqBQ7JNMNJ65MQg3kXiAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"244073f0eb75335f1388fa97b0679f83eea5e05e1e535e54cfd0f6ab1aa6b4e9","last_reissued_at":"2026-05-18T00:12:48.229446Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:48.229446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.08881","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:12:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RNbeLWrbJCiAke2Y4lkI56xPna6wYW9RCSsqWZDEfxD302ZudyAXTVuPQiKrC9TUJvRrEWaOHbjXfaAeDRGXBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T02:37:36.897054Z"},"content_sha256":"571ecfae3d0132b76ba99b0580ab30ce2b2a0b4595dc9064564709c261931f0b","schema_version":"1.0","event_id":"sha256:571ecfae3d0132b76ba99b0580ab30ce2b2a0b4595dc9064564709c261931f0b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ERAHH4HLOUZV6E4I7KL3AZ47QP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Langlands parameter of a simple supercuspidal representation: Symplectic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Eyal Kaplan, Moshe Adrian","submitted_at":"2018-03-23T16:55:29Z","abstract_excerpt":"Let $\\pi$ be a simple supercuspidal representation of the symplectic group $Sp_{2l}(F)$, over a $p$-adic field $F$. In this work, we explicitly compute the Rankin-Selberg $\\gamma$-factor of rank-$1$ twists of $\\pi$. We then completely determine the Langlands parameter of $\\pi$, if $p \\neq 2$. In the case that $F = \\mathbb{Q}_2$, we give a conjectural description of the functorial lift of $\\pi$, with which, using a recent work of Bushnell and Henniart, one can obtain its Langlands parameter."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.08881","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:12:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AatN21/FStNNl8bV6oVu4dTX/jL4R9ZFdeIkWls2HL0r1sH9d71Oi0Ls5wBy9pKzUKkSz/sCADXVcng3Om3qCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T02:37:36.897706Z"},"content_sha256":"22c3f87a742d8c4ae222bf2f436d2ea988e89465f3b886257378626fc69d4853","schema_version":"1.0","event_id":"sha256:22c3f87a742d8c4ae222bf2f436d2ea988e89465f3b886257378626fc69d4853"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ERAHH4HLOUZV6E4I7KL3AZ47QP/bundle.json","state_url":"https://pith.science/pith/ERAHH4HLOUZV6E4I7KL3AZ47QP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ERAHH4HLOUZV6E4I7KL3AZ47QP/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-07T02:37:36Z","links":{"resolver":"https://pith.science/pith/ERAHH4HLOUZV6E4I7KL3AZ47QP","bundle":"https://pith.science/pith/ERAHH4HLOUZV6E4I7KL3AZ47QP/bundle.json","state":"https://pith.science/pith/ERAHH4HLOUZV6E4I7KL3AZ47QP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ERAHH4HLOUZV6E4I7KL3AZ47QP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ERAHH4HLOUZV6E4I7KL3AZ47QP","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f62b276b06576984343e6eac4948220295a0d86ba815b13ff97def2bc738c070","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-03-23T16:55:29Z","title_canon_sha256":"6cff6fbc0d7ea809a1460a9e403efc846d5ccd646cd8df5930ea819ff3bc3226"},"schema_version":"1.0","source":{"id":"1803.08881","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.08881","created_at":"2026-05-18T00:12:48Z"},{"alias_kind":"arxiv_version","alias_value":"1803.08881v2","created_at":"2026-05-18T00:12:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.08881","created_at":"2026-05-18T00:12:48Z"},{"alias_kind":"pith_short_12","alias_value":"ERAHH4HLOUZV","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"ERAHH4HLOUZV6E4I","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"ERAHH4HL","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:22c3f87a742d8c4ae222bf2f436d2ea988e89465f3b886257378626fc69d4853","target":"graph","created_at":"2026-05-18T00:12:48Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $\\pi$ be a simple supercuspidal representation of the symplectic group $Sp_{2l}(F)$, over a $p$-adic field $F$. In this work, we explicitly compute the Rankin-Selberg $\\gamma$-factor of rank-$1$ twists of $\\pi$. We then completely determine the Langlands parameter of $\\pi$, if $p \\neq 2$. In the case that $F = \\mathbb{Q}_2$, we give a conjectural description of the functorial lift of $\\pi$, with which, using a recent work of Bushnell and Henniart, one can obtain its Langlands parameter.","authors_text":"Eyal Kaplan, Moshe Adrian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-03-23T16:55:29Z","title":"The Langlands parameter of a simple supercuspidal representation: Symplectic groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.08881","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:571ecfae3d0132b76ba99b0580ab30ce2b2a0b4595dc9064564709c261931f0b","target":"record","created_at":"2026-05-18T00:12:48Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f62b276b06576984343e6eac4948220295a0d86ba815b13ff97def2bc738c070","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-03-23T16:55:29Z","title_canon_sha256":"6cff6fbc0d7ea809a1460a9e403efc846d5ccd646cd8df5930ea819ff3bc3226"},"schema_version":"1.0","source":{"id":"1803.08881","kind":"arxiv","version":2}},"canonical_sha256":"244073f0eb75335f1388fa97b0679f83eea5e05e1e535e54cfd0f6ab1aa6b4e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"244073f0eb75335f1388fa97b0679f83eea5e05e1e535e54cfd0f6ab1aa6b4e9","first_computed_at":"2026-05-18T00:12:48.229446Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:48.229446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jt45jYbllqchnhZFS6+AtgwFYHOg6Uy+rS9HxhG+exeWPAMTd7qwXf+BOGfc7furMZqBQ7JNMNJ65MQg3kXiAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:48.230068Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.08881","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:571ecfae3d0132b76ba99b0580ab30ce2b2a0b4595dc9064564709c261931f0b","sha256:22c3f87a742d8c4ae222bf2f436d2ea988e89465f3b886257378626fc69d4853"],"state_sha256":"8e61030b65ef047328ea4528cdd22a58ee4565e166f12d949bef3ce081cbfe1b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cdUMUcMnsR0dPnaiJW1Z0VCURBxEONYf7eHtKlYOYj9Wa+GU7xdpyEiEdRz6ZQCphmsYqJLiyUzNr0xS9Fo+AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T02:37:36.900740Z","bundle_sha256":"4fafc977f285e62bd5227d6547c61814da0395120ced875029746423dadd42eb"}}